论文标题
大量有限领域中的权力总和：方法的混合
Sums of Powers in Large Finite Fields: A Mix of Methods
论文作者
论文摘要
足够大的有限字段中的任何元素是否可以表示为该领域的两个$ d $ thers的总和？在本文中，我们叙述了这个问题的一些历史，涉及了循环切开术，费马特的最后一个定理和对角线方程。然后，我们根据傅立叶分析和有限领域理论的非平凡估计的应用，提供两个新的和基本的证据，一个更古典的证据，而另一个则更古典。在上下文和并置，每个人都具有其优点。
Can any element in a sufficiently large finite field be represented as a sum of two $d$th powers in the field? In this article, we recount some of the history of this problem, touching on cyclotomy, Fermat's last theorem, and diagonal equations. Then, we offer two proofs, one new and elementary, and the other more classical, based on Fourier analysis and an application of a nontrivial estimate from the theory of finite fields. In context and juxtaposition, each will have its merits.
